A team of researchers led by Professors of Mathematics Tony Pantev and Ron Donagi have received a $10 million Simons Collaboration Grant to prove the Homological Mirror Symmetry Conjecture, one of mathematics’ outstanding open problems. Solving this has potential applications in fields from particle physics to geometry.

“Homological mirror symmetry has generated a lot of deep research and interesting theorems,” says Pantev. “The ideas have gestated enough that we can really push and converge on a method that would solve it.”

The conjecture concerns what are called Calabi-Yau spaces, tiny, six-dimensional curved spaces whose properties were originally hypothesized in 1957 by Eugenio Calabi, a now-retired Penn mathematician, and proven 21 years later by Shing-Tung Yau. According to string theory, all matter is made up of vibrating strings wrapped around these Calabi-Yau spaces, strings that create musical notes we “hear” as electrons, protons, photons, and gravitons. It did not take long for physicists to realize the overwhelming importance of these spaces in string theory.